climbing_ucsas.knit

.title[
# <div class="line-block">4 (3) years later: A look back at the sport climbing competition format and scoring system at Tokyo 2020 (2021)</div>
]
.subtitle[
## Quang Nguyen
]
.institute[
### UCSAS 2024
]
.date[
### <svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg> qntkhvn       <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg> <span class="citation">@qntkhvn</span>       <svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M579.8 267.7c56.5-56.5 56.5-148 0-204.5c-50-50-128.8-56.5-186.3-15.4l-1.6 1.1c-14.4 10.3-17.7 30.3-7.4 44.6s30.3 17.7 44.6 7.4l1.6-1.1c32.1-22.9 76-19.3 103.8 8.6c31.5 31.5 31.5 82.5 0 114L422.3 334.8c-31.5 31.5-82.5 31.5-114 0c-27.9-27.9-31.5-71.8-8.6-103.8l1.1-1.6c10.3-14.4 6.9-34.4-7.4-44.6s-34.4-6.9-44.6 7.4l-1.1 1.6C206.5 251.2 213 330 263 380c56.5 56.5 148 56.5 204.5 0L579.8 267.7zM60.2 244.3c-56.5 56.5-56.5 148 0 204.5c50 50 128.8 56.5 186.3 15.4l1.6-1.1c14.4-10.3 17.7-30.3 7.4-44.6s-30.3-17.7-44.6-7.4l-1.6 1.1c-32.1 22.9-76 19.3-103.8-8.6C74 372 74 321 105.5 289.5L217.7 177.2c31.5-31.5 82.5-31.5 114 0c27.9 27.9 31.5 71.8 8.6 103.9l-1.1 1.6c-10.3 14.4-6.9 34.4 7.4 44.6s34.4 6.9 44.6-7.4l1.1-1.6C433.5 260.8 427 182 377 132c-56.5-56.5-148-56.5-204.5 0L60.2 244.3z"/></svg> qntkhvn.netlify.app
]

---

<p style="font-size:3.8em">
<b>
Sport Climbing at Tokyo 2020
</b>
</p>

---

# Competition & Scoring

-   Sport climbing made its Olympic debut at Tokyo 2020

-   3 disciplines: speed climbing, bouldering, lead climbing

-   Only 1 set of medals for each gender at the Olympics

-   Combined scoring system: multiplying 3 disciplines' ranks (best score = lowest score)

-   Example: `\(1\)`st in speed `\(\times\)` `\(5\)`th in bouldering `\(\times\)` `\(7\)`th in lead `\(=\)` total score of `\(35\)`

-   2 rounds: qualification (20 climbers), final (top 8 from qualification)

---

# Concerns

*   Climber interviews with Climbing Magazine in 2016:

> "I am NOT in support of the format that imposes that all climbers must compete in speed climbing. That is like asking a middle distance runner to compete in the sprint. Speed climbing is a sport within our sport." - Lynn Hill, former US Climber.

> "Honestly, the people that will suffer the most are the ones that focus only on speed climbing. Those skills/abilities don’t transfer as well to the other disciplines." - Mike Doyle, US Climber.

*   Words and phrases: "bogus", "a bummer", "less than ideal", "not in support", "cheesy and unfair".

---

# Investigation Questions

**What are the properties and limitations of the sport climbing "triathlon" format and rank-product scoring?**

*   What are the probabilities of qualifying/winning, given certain placements?
    
*   What are the expected placement scores for each round?

*   Are the concerns of the climbers valid?

---

<p style="font-size:3.8em">
<b>
Simulation Study
</b>
</p>

---

#   Assumptions

*     Within-discipline uniform ranks

*     Between-discipline correlation

*   Simulate from a calibrated copula with a specified dependence structure
      
      *   Incorporate correlation (Kendall's `\(\tau\)`) between bouldering and lead obtained from empirical data
      
      *   Speed is assumed independent of bouldering and lead

---

#   Simulation results: Win Probability vs Correlation

.pull-left[
As bouldering-lead correlation increases, the overall win probability
* increases, given a boulder/lead victory
* decreases, given a speed victory
    
When bouldering and lead are perfectly correlated, the gold medal probability
* only ~20.5% for winning speed
* ~90.3% for winning boulder/lead
]

.pull-right[
<img src="data:image/png;base64,#climbing_ucsas_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" />
]

---

#   Simulation results: Placement Probabilities

Given that a climber wins any discipline...

*   For a qualifier, what is the probability of qualifying for final (finishing at 8 or better)? &nbsp; &nbsp; `\(99.5\%\)`

*   For a finalist, what is the probability of winning a medal (finishing in top 3)? &nbsp; &nbsp; `\(84.8\%\)`

]

.pull-right[
<img src="data:image/png;base64,#climbing_ucsas_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" />
]

---

#   Simulation results: Placement Scores

*   For qualifiers: `\(453\)` to make top `\(8\)`
    
    *   For finalists:  `\(9, 19, 33\)` to win gold, silver, bronze
]    
    
.pull-right[
<img src="data:image/png;base64,#climbing_ucsas_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" />
]

---

<p style="font-size:3.8em">
<b>
Correlation Analysis
</b>
</p>

---

# Rank Correlation

-   Correlations between the overall rank and the ranks of the individual disciplines (speed, bouldering, and lead)

-   Case study: Tokyo 2020 Women's Qualification

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<table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
  <thead>
    
    <tr class="gt_col_headings">
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="climber">climber</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="overall">overall</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="speed">speed</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="bouldering">bouldering</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="lead">lead</th>
    </tr>
  </thead>
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    <tr><td headers="climber" class="gt_row gt_left">Janja Garnbret</td>
<td headers="overall" class="gt_row gt_right">1</td>
<td headers="speed" class="gt_row gt_right">14</td>
<td headers="bouldering" class="gt_row gt_right">1</td>
<td headers="lead" class="gt_row gt_right">4</td></tr>
    <tr><td headers="climber" class="gt_row gt_left">Seo Chae-hyun</td>
<td headers="overall" class="gt_row gt_right">2</td>
<td headers="speed" class="gt_row gt_right">17</td>
<td headers="bouldering" class="gt_row gt_right">5</td>
<td headers="lead" class="gt_row gt_right">1</td></tr>
    <tr><td headers="climber" class="gt_row gt_left">Miho Nonaka</td>
<td headers="overall" class="gt_row gt_right">3</td>
<td headers="speed" class="gt_row gt_right">4</td>
<td headers="bouldering" class="gt_row gt_right">8</td>
<td headers="lead" class="gt_row gt_right">3</td></tr>
    <tr><td headers="climber" class="gt_row gt_left">Akiyo Noguchi</td>
<td headers="overall" class="gt_row gt_right">4</td>
<td headers="speed" class="gt_row gt_right">9</td>
<td headers="bouldering" class="gt_row gt_right">3</td>
<td headers="lead" class="gt_row gt_right">6</td></tr>
    <tr><td headers="climber" class="gt_row gt_left">Brooke Raboutou</td>
<td headers="overall" class="gt_row gt_right">5</td>
<td headers="speed" class="gt_row gt_right">12</td>
<td headers="bouldering" class="gt_row gt_right">2</td>
<td headers="lead" class="gt_row gt_right">8</td></tr>
  </tbody>
  
  
</table>
</div>

---

# Rank Correlation

**Lead** and **bouldering** ranks are more highly correlated with **overall** rank than **speed**.

<img src="data:image/png;base64,#climbing_ucsas_files/figure-html/unnamed-chunk-6-1.png" width="612" style="display: block; margin: auto;" />
]

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      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="Kendall">Kendall</th>
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<td headers="Kendall" class="gt_row gt_right">0.147</td>
<td headers="p-value" class="gt_row gt_right">0.386</td>
<td headers="Bootstrapped 95% CI" class="gt_row gt_left">(−0.191, 0.469)</td></tr>
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<td headers="p-value" class="gt_row gt_right">0.004</td>
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</div>

]

---

# Principal component analysis

-   Visualize underlying correlations that exist among the climbing discipline performances

-   Speed race time

-   Bouldering tops

-   Lead holds
]

-   Case study: Tokyo 2020 Women's Qualification

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    <tr><td headers="climber" class="gt_row gt_left">Janja Garnbret</td>
<td headers="speed_time" class="gt_row gt_right">9.44</td>
<td headers="bould_tops" class="gt_row gt_right">4</td>
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    <tr><td headers="climber" class="gt_row gt_left">Seo Chae-hyun</td>
<td headers="speed_time" class="gt_row gt_right">10.01</td>
<td headers="bould_tops" class="gt_row gt_right">2</td>
<td headers="lead_holds" class="gt_row gt_right">40.5</td></tr>
    <tr><td headers="climber" class="gt_row gt_left">Miho Nonaka</td>
<td headers="speed_time" class="gt_row gt_right">7.55</td>
<td headers="bould_tops" class="gt_row gt_right">1</td>
<td headers="lead_holds" class="gt_row gt_right">30.5</td></tr>
    <tr><td headers="climber" class="gt_row gt_left">Akiyo Noguchi</td>
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<td headers="bould_tops" class="gt_row gt_right">3</td>
<td headers="lead_holds" class="gt_row gt_right">27.5</td></tr>
    <tr><td headers="climber" class="gt_row gt_left">Brooke Raboutou</td>
<td headers="speed_time" class="gt_row gt_right">8.67</td>
<td headers="bould_tops" class="gt_row gt_right">3</td>
<td headers="lead_holds" class="gt_row gt_right">26.5</td></tr>
    <tr><td headers="climber" class="gt_row gt_left">Jessica Pilz</td>
<td headers="speed_time" class="gt_row gt_right">8.51</td>
<td headers="bould_tops" class="gt_row gt_right">1</td>
<td headers="lead_holds" class="gt_row gt_right">33.5</td></tr>
    <tr><td headers="climber" class="gt_row gt_left">Aleksandra Mirosław</td>
<td headers="speed_time" class="gt_row gt_right">6.97</td>
<td headers="bould_tops" class="gt_row gt_right">0</td>
<td headers="lead_holds" class="gt_row gt_right">12.0</td></tr>
  </tbody>
  
  
</table>
</div>
]

---

# Principal component analysis

*   Strong and positive correlation between bouldering and lead performances

*   Speed time is completely separated from other two performance variables

**The competition format is stacked against speed climbers**

]

]

---

<p style="font-size:3.8em">
<b>
Leave-one-climber-out Analysis
</b>
</p>

---

# Independence of irrelevant alternatives

**What would happen to the overall rankings (in particular, order of medalists) if one climber got disqualified?**

-   This has a connection with the independence of irrelevant alternatives (IIA)

-   IIA: rank orderings should not change if a losing candidate is removed and the scores are re-calculated

-   There's evidence for a violation of the IIA property from real data.

---

# IIA Violation

Panel 5: If 5th-place climber (Krasovskaia) was excluded, climber with actual rank 4 (Meul) would move up to 2nd!!!

---

<p style="font-size:3.8em">
<b>
Takeaways
</b>
</p>

---

# Discussion

-   The idea of a climbing triathlon gives speed climbers a huge disadvantage.

-   The independence of irrelevant alternatives is violated, which is an issue of rank-product scoring.

-   Solution: 1 set of medals for speed and 1 set of medals for bouldering and lead.

-   It is confirmed that at Paris 2024, there will be 2 sets of medals:

-   Lead and bouldering, combined
    
    -   Speed-only event

---

# Acknowledgements

Hannah Butler <br>Colorado State University

]

![](data:image/png;base64,#greg.gif)

Gregory J. Matthews <br>Loyola University Chicago

]

---

# How it started

<blockquote class="twitter-tweet"><p lang="en" dir="ltr"><a href="https://twitter.com/qntkhvn?ref_src=twsrc%5Etfw">@qntkhvn</a> Yo. I have an idea for a quick paper. We could probably write it up as a note in like a week. It&#39;s about the scoring system in sport climbing. Any interest?</p>&mdash; Volume Tweeter (@StatsInTheWild) <a href="https://twitter.com/StatsInTheWild/status/1411033054890500096?ref_src=twsrc%5Etfw">July 2, 2021</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>

]

]

---

# UCSAS 2021

<blockquote class="twitter-tweet"><p lang="en" dir="ltr"><a href="https://twitter.com/hashtag/UCSAS2021?src=hash&amp;ref_src=twsrc%5Etfw">#UCSAS2021</a> poster on sport climbing&#39;s combined competition format and rank-product scoring system, joint work with @neighboringCity and <a href="https://twitter.com/StatsInTheWild?ref_src=twsrc%5Etfw">@StatsInTheWild</a>. <br><br>GitHub: <a href="https://t.co/Omq7v52lbr">https://t.co/Omq7v52lbr</a><br>Series of climbing blog posts: <a href="https://t.co/FRjJS14Bqw">https://t.co/FRjJS14Bqw</a><a href="https://twitter.com/hashtag/RStats?src=hash&amp;ref_src=twsrc%5Etfw">#RStats</a> <a href="https://twitter.com/hashtag/sportsanalytics?src=hash&amp;ref_src=twsrc%5Etfw">#sportsanalytics</a> <a href="https://t.co/t9G0PKzLh0">pic.twitter.com/t9G0PKzLh0</a></p>&mdash; qntkhvn (@qntkhvn) <a href="https://twitter.com/qntkhvn/status/1445765942969978888?ref_src=twsrc%5Etfw">October 6, 2021</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>

</center>

---

# Related links

<center>
<big>
Cheers.
</big>
</centeR>